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Bias-corrected bootstrap prediction regions for vector autoregression

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  • Jae H. Kim

    (Department of Econometrics and Business Statistics, Monash University, Caulfield East, Victoria 3145, Australia)

Abstract

This paper examines small sample properties of alternative bias-corrected bootstrap prediction regions for the vector autoregressive (VAR) model. Bias-corrected bootstrap prediction regions are constructed by combining bias-correction of VAR parameter estimators with the bootstrap procedure. The backward VAR model is used to bootstrap VAR forecasts conditionally on past observations. Bootstrap prediction regions based on asymptotic bias-correction are compared with those based on bootstrap bias-correction. Monte Carlo simulation results indicate that bootstrap prediction regions based on asymptotic bias-correction show better small sample properties than those based on bootstrap bias-correction for nearly all cases considered. The former provide accurate coverage properties in most cases, while the latter over-estimate the future uncertainty. Overall, the percentile-t bootstrap prediction region based on asymptotic bias-correction is found to provide highly desirable small sample properties, outperforming its alternatives in nearly all cases. Copyright © 2004 John Wiley & Sons, Ltd.

Suggested Citation

  • Jae H. Kim, 2004. "Bias-corrected bootstrap prediction regions for vector autoregression," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(2), pages 141-154.
    • Handle: RePEc:jof:jforec:v:23:y:2004:i:2:p:141-154
    DOI: 10.1002/for.908
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    References listed on IDEAS

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    1. Matteo Grigoletto, 1998. "Bootstrap prediction intervals for autoregressive models fitted to non-autoregressive processes," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 7(3), pages 285-295, December.
    2. Kim, Jae H, 2001. "Bootstrap-after-Bootstrap Prediction Intervals for Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 117-128, January.
    3. Chatfield, Chris, 1993. "Calculating Interval Forecasts: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 143-144, April.
    4. Masarotto, Guido, 1990. "Bootstrap prediction intervals for autoregressions," International Journal of Forecasting, Elsevier, vol. 6(2), pages 229-239, July.
    5. Paul Kabaila, 1993. "On Bootstrap Predictive Inference For Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(5), pages 473-484, September.
    6. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-135, April.
    7. Clements, Michael P. & Taylor, Nick, 2001. "Bootstrapping prediction intervals for autoregressive models," International Journal of Forecasting, Elsevier, vol. 17(2), pages 247-267.
    8. Kim, Jae H., 1997. "Relationship Between the Forward and Backward Representations of the Stationary VAR Model," Econometric Theory, Cambridge University Press, vol. 13(06), pages 889-889, December.
    9. Lutz Kilian, 1998. "Confidence intervals for impulse responses under departures from normality," Econometric Reviews, Taylor & Francis Journals, vol. 17(1), pages 1-29.
    10. Kent D. Wall & David S. Stoffer, 2002. "A State space approach to bootstrapping conditional forecasts in arma models," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(6), pages 733-751, November.
    11. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2001. "Effects of parameter estimation on prediction densities: a bootstrap approach," International Journal of Forecasting, Elsevier, vol. 17(1), pages 83-103.
    12. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May.
    13. Kim, Jae H., 1999. "Asymptotic and bootstrap prediction regions for vector autoregression," International Journal of Forecasting, Elsevier, vol. 15(4), pages 393-403, October.
    14. Grigoletto, Matteo, 1998. "Bootstrap prediction intervals for autoregressions: some alternatives," International Journal of Forecasting, Elsevier, vol. 14(4), pages 447-456, December.
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    Cited by:

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    2. Ruiz Ortega, Esther & Fresoli, Diego Eduardo & Pascual, Lorenzo, 2011. "Bootstrap forecast of multivariate VAR models without using the backward representation," DES - Working Papers. Statistics and Econometrics. WS ws113426, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Daniel Grabowski & Anna Staszewska-Bystrova & Peter Winker, 2020. "Skewness-adjusted bootstrap confidence intervals and confidence bands for impulse response functions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 5-32, March.
    4. Winker, Peter & Helmut, Lütkepohl & Staszewska-Bystrova, Anna, 2014. "Confidence Bands for Impulse Responses: Bonferroni versus Wald," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100597, Verein für Socialpolitik / German Economic Association.
    5. Bruns, Martin & Lütkepohl, Helmut, 2022. "Comparison of local projection estimators for proxy vector autoregressions," Journal of Economic Dynamics and Control, Elsevier, vol. 134(C).
    6. Liu, Shen & Maharaj, Elizabeth Ann & Inder, Brett, 2014. "Polarization of forecast densities: A new approach to time series classification," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 345-361.
    7. Tom Engsted & Thomas Q. Pedersen, 2014. "Bias-Correction in Vector Autoregressive Models: A Simulation Study," Econometrics, MDPI, vol. 2(1), pages 1-27, March.
    8. Anna Staszewska‐Bystrova, 2011. "Bootstrap prediction bands for forecast paths from vector autoregressive models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(8), pages 721-735, December.
    9. Fresoli, Diego & Ruiz, Esther & Pascual, Lorenzo, 2015. "Bootstrap multi-step forecasts of non-Gaussian VAR models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 834-848.
    10. Jing, Li, 2009. "Bootstrap prediction intervals for threshold autoregressive models," MPRA Paper 13086, University Library of Munich, Germany.
    11. Anna Staszewska-Bystrova, 2009. "Bootstrap Confidence Bands for Forecast Paths," Working Papers 024, COMISEF.
    12. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    13. Li, Jing, 2011. "Bootstrap prediction intervals for SETAR models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 320-332, April.
    14. Mulubrhan G. Haile & Lingling Zhang & David J. Olive, 2024. "Predicting Random Walks and a Data-Splitting Prediction Region," Stats, MDPI, vol. 7(1), pages 1-11, January.
    15. Li, Jing, 2011. "Bootstrap prediction intervals for SETAR models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 320-332.
    16. Staszewska-Bystrova, Anna & Winker, Peter, 2013. "Constructing narrowest pathwise bootstrap prediction bands using threshold accepting," International Journal of Forecasting, Elsevier, vol. 29(2), pages 221-233.

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